OVER THE BAY OF BENGAL — Aboard a U.S. Navy P-8A Poseidon, the U.S. military's most advanced maritime surveillance aircraft, the nine-man crew scoured a swath of sea some 7,500 square miles—an area bigger than New Jersey—in the hopes of finding Malaysia Airlines Flight 370.

From the window, the sea and sky smudged together in an indistinguishable gray blur, and every white wave-top appeared momentarily to the untrained eye to be something important. But the crew found no evidence of the missing plane on Sunday, having...